The sphere packing problem in dimension 24

Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.

• Publication year

  2016

• Venue

  arXiv: Number Theory

• Publication date

  2016-03-21

• Fields of study

  Mathematics

• Identifiers
  DOI 10.4007/annals.2017.185.3.8arXiv 1603.06518
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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